The chief constable of West Yorkshire police, Sir Norman Bettison, "boasted" about having helped to "concoct" a false account of how the 1989 Hillsborough disaster was caused, according to the Labour MP Maria Eagle.

Speaking in a parliamentary debate following last month's publication of the Hillsborough Independent Panel's report, Eagle cited a letter written by John Barry, who studied with Bettison on a part-time course at Sheffield Business School while Bettison was serving with South Yorkshire police.

Nine years later, Barry wrote to the Hillsborough Family Support Group's solicitor, Ann Adlington, a letter which he gave Eagle permission to make public, with parliamentary privilege, in the debate. Barry said Bettison discussed his role within South Yorkshire police weeks after the disaster of 15 April 1989, in which 96 Liverpool supporters died.

Barry wrote: "We were in a pub after our weekly evening class. [Bettison] told me that he had been asked by his senior officers to put together the South Yorkshire police evidence for the forthcoming inquiry. He said that 'we are trying to concoct a story that all the Liverpool fans were drunk and we were afraid that they were going to break down the gates so we decided to open them'."

That was the version of events South Yorkshire police put forward to the official inquiry into Hillsborough by Lord Justice Taylor, and to the inquest into the deaths. Taylor, and the panel in its report, found that account was untrue, that there was no excessive drinking or misbehaviour by the supporters, and in fact the police mismanaged the crowd on the day.

Bettison's name appeared on internal South Yorkshire police documents which led to Eagle naming him in 1998 as a member of what she termed a "black propaganda" campaign within South Yorkshire police to shift the blame from their own failings for Hillsborough falsely on to supporters. He always denied any involvement in smearing Liverpool supporters or what is now labelled the police's "cover-up."

But after the publication of the panel's report, West Yorkshire police referred Bettison, who is still their serving chief constable, to the Independent Police Complaints Commission for possible misconduct. Bettison, having at first said the report exonerated him, announced he is to retire from policing in March.

The bereaved families have felt particularly aggrieved about Bettison's involvement in the post-Hillsborough operation within South Yorkshire police because in 1998, shortly after first being named by Eagle in parliament, he was appointed chief constable of Merseyside police.

Eagle said of the letter from Barry, who was at Hillsborough as a supporter: "Here we have an account of a contemporaneous conversation in which Norman Bettison boasted he is engaged in a South Yorkshire police plot to fit up the Liverpool fans and deflect blame from the force. That is indeed what happened subsequently, so what Sir Norman denies in public he boasts about in private conversations."

During a long and at times emotional debate, it emerged that the IPCC has been given the names of 1,444 officers for possible investigation in relation to Hillsborough, including 304 who are still serving. Keith Vaz, Labour chairman of the home affairs select committee, raised concerns about whether the watchdog has sufficient resources.

The director of public prosecutions, Keir Starmer QC, alongside the IPCC, is examining all the evidence revealed by the panel to see whether criminal charges should be brought against any corporate body or individuals.

Andy Burnham, the shadow health secretary, closed the debate for Labour by paying tribute to the Hillsborough families, who had fought 23 years for the truth about the disaster to be accepted. Burnham said the disaster itself, then the dissemination of the false accounts, and the length of time it had taken to dispel them, represented failure by the football authorities, media, police and parliament, bodies which must all learn lessons so such failures are never repeated.